S&W's current .44 Special cylinders are longer than the M-24-3 and M-624 (and earlier models) cylinders. They won't fit without major reworking, being shortened on the front face at least. A gunsmith with a lathe and the correct knowledge could trim a new one down, or modify some other cylinder to fit, or remove the rear portion of the barrel to match up with the new cylinder, but it would be a good bit of labor and be fairly pricey, time being money.

Does anyone know of any Model 624 that had the cylinder fail? I don't believe I have ever heard of one.

You may be ahead of the game to sell it to someone "as is" willing to run the risk, and either finding one in the box with the "C" or buying an early M-629 .44 Magnum Mountain Gun.